Gröbner-Shirshov basis for degenerate Ringel-Hall algebras of type <Emphasis Type="Italic">F</Emphasis><Subscript>4</Subscript>

In this paper, by using the Frobenius morphism and the multiplication formulas of the generic extension monoid algebra, the authors first give a presentation of the degenerate Ringel-Hall algebra, and then construct the Gröbner-Shirshov basis for degenerate Ringel-Hall algebras of type F ₄.     

Structural modification on rupestonic acid leads to highly potent inhibitors against influenza virus

Molecular Diversity - Influenza viruses are responsible for seasonal epidemics and occasional pandemics, which cause significant morbidity and mortality. Although several drugs (adamantanes and...     

D4型量子包络代数的Gelfand-Kirillov维数

本文研究了D₄ 型量子包络代数的Gelfand-Kirillov 维数的计算问题. 利用文献[1] 中给出的Gelfand-Kirillov 维数的计算方法和文献[2] 中给出的D₄ 型量子包络代数的Groebner-Shirshov 基计算了D₄型量子包络代数的Gelfand-Kirillov 维数, 得到的主要结果是D₄ 型量子包络代数的Gelfand-Kirillov 维数为28. 希望此结果为计算D_n型量子包络代数的Gelfand-Kirillov 维数提供一些思路.     

Generalized tilting functors and Ringel-Hall algebras

It is known from [M. Auslander, M.I. Platzeck, I. Reiten, Coxeter functors without diagrams, Trans. Amer. Math. Soc. 250 (1979) 1-46] and [C.M. Ringel, PBW-basis of quantum groups, J. Reine Angew. Math. 470 (1996) 51-85] that the Bernstein-Gelfand-Ponomarev reflection functors are special cases of tilting functors and these reflection functors induce isomorphisms between certain subalgebras of Ringel-Hall algebras. In [A. Wufu, Tilting functors and Ringel-Hall algebras, Comm. Algebra 33 (1) (2005) 343-348] the result from [C.M. Ringel, PBW-basis of quantum groups, J. Reine Angew. Math. 470 (1996) 51-85] is generalized to the tilting module case by giving an isomorphism between two Ringel-Hall subalgebras. In [J. Miyashita, Tilting Modules of Finite Projective Dimension, Math. Z. 193 (1986) 113-146] Miyashita generalized the tilting theory by introducing the tilting modules of finite projective dimension. In this paper the result in [A. Wufu, Tilting functors and Ringel-Hall algebras, Comm. Algebra 33 (1) (2005) 343-348] is generalized to the tilting modules of finite projective dimension.     

火焰原子吸收光度法测定维药芜菁的微量元素

为探讨微量元素与芜菁的药效关系,用火焰原子吸收分光光度法测定了维药芜菁中的K,Na,Ca,Fe,Cu,Co,Zn,Mn,Mg等9种元素含量。结果表明,芜菁含有丰富的人体必需微量元素,其中K,Na,Ca,Zn的含量更显著;方法的回收率在93．7％～102．5％之间,RSD值在0．39％-1．3％之间,能用于维药芜菁中多种微量元素的同时测定。为芜菁的进一步研究和综合开发利用提供了新的科学依据。     

Skew-commutator relations and Gröbner-Shirshov basis of quantum group of type F 4

We give a Grobner-Shirshov basis of quantum group of type F4 by using the Ringel-Hall algebra approach. We compute all skew-commutator relations between the isoclasses of indecomposable representations of Ringel- Hall algebras of type F4 by using an ＇inductive＇ method. Precisely, we do not use the traditional way of computing the skew-commutative relations, that is first compute all Hall polynomials then compute the corresponding skew- commutator relations; instead, we compute the ＇easier＇ skew-commutator relations which correspond to those exact sequences with middle term indecomposable or the split exact sequences first, then ＇deduce＇ others from these ＇easier＇ ones and this in turn gives Hall polynomials as a byproduct. Then using the composition-diamond lemma prove that the set of these relations constitute a minimal CrSbner-Shirshov basis of the positive part of the quantum group of type F4. Dually, we get a Grobner-Shirshov basis of the negative part of the quantum group of type F4. And finally, we give a Gr6bner-Shirshov basis for the whole quantum group of type F4.     

Grbner-Shirshov Basis and the Minimal Projective Resolution of U_q~+(G_2)

In this paper, by using the Anick's resolution and Gröbner-Shirshov basis for quantized enveloping algebra of type G₂, we compute the minimal projective resolution of the trivial module of U_q⁺ (G₂) and as an application we compute the global dimension of U_q⁺ (G₂).     

Synthesis and Antiviral Activity of New Derivatives of Rupestonic Acid

Chemistry of Natural Compounds - A series of 20 new derivatives of rupestonic acid were synthesized via Davis oxidation. Their antiviral activity against influenza A virus (H3N2) was established....     

The Skew-commutator Relations and Gröbner-Shirshov Bases of Quantum Group of Type C3

Acta Mathematicae Applicatae Sinica, English Series - In this paper, we give a Gröbner-Shirshov basis of quantum group of type ℂ3 by using the Ringel-Hall algebra approach. For this,...     

ResBos and ePump Analysis on ATLAS 8TeV Z Boson Transverse Momentum Distributions

International Journal of Theoretical Physics - Fixed-order predictions cannot describe the vector boson production process in low transverse momentum regions where resummation of soft gluon...